Problem: A cube of mass 2 kg is held stationary against a rough wall by a force F = 40 N passing through center C. Find the perpendicular distance of normal reaction between the wall and cube from point C. The side of the cube is 20 cm.

Understanding the problem: The problem involves finding the perpendicular distance of the normal reaction between the wall and the cube from point C. The cube is held stationary against the wall by a force F = 40 N passing through center C. The side of the cube is 20 cm.

Solution:
To solve this problem, we need to use the concept of torque and equilibrium. The torque of the force F about point C should be equal and opposite to the torque of the normal reaction about point C for the cube to be in equilibrium. Let us assume that the perpendicular distance of the normal reaction from point C is d.

Calculations:
Torque due to force F = F x r = 40 N x 0.1 m = 4 Nm (where r is the distance of force F from point C)
Torque due to normal reaction = N x d (where N is the normal reaction)

Since the cube is in equilibrium, the torques due to force F and normal reaction should be equal and opposite.
Therefore, N x d = 4 Nm
N = 4/d

To find the value of d, we need to use the concept of friction. The cube is held stationary against the wall, which means that the force of friction acting on the cube is equal and opposite to the force F. The maximum force of friction can be calculated as follows:

Frictional force (f) = coefficient of friction (μ) x normal reaction (N)
Since the cube is just about to move, the frictional force should be equal to the force F.
Therefore, f = F = 40 N
μ x N = 40 N
μ x 4/d = 40 N
μ = 10/d

The coefficient of friction depends on the surface and the materials involved. Let us assume that the coefficient of friction between the cube and the wall is 0.5. Therefore, μ = 0.5.

μ x 4/d = 40 N
0.5 x 4/d = 40 N
d = 0.1 m = 10 cm

Therefore, the perpendicular distance of the normal reaction between the wall and the cube from point C is 10 cm.

Conclusion: The perpendicular distance of the normal reaction between the wall and the cube from point C is 10 cm.

10cm. coz normal acts on the centre of mass and for the uniform cube the centre of mass if at 10cm from the middle of one of the edge. the wall is in contact with one of the face of the cube.